VARIATION  OF  ELECTRICAL  RESISTANCE  IN  THE 

MAGNETIC  FIELD 


BY 

WILLIAM  HOWARD  SANDERS 

A.B.  University  of  Illinois,  1920 


THESIS 

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IN  THE  GRADUATE  SCHOOL  OF  THE  UNIVERSITY 
OF  ILLINOIS,  1922 


URBANA,  ILLINOIS 


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UNIVERSITY  OF  ILLINOIS 


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CONTENTS 

I Origin  and  Scope  1 

II  Historical  Review  of  Experimental  Study  2 

III  Theoretical  Treatments  11 

IV  Suggestive  Experiments,  Their  Bearing  on  the  Theory  16 

V Experimental  Work  Here  19 

VI  Discussion  25 

Bibliography  27 

Table  1 Observations  on  the  Resistance  Change  of  #40 
B & S Copper  Wire  in  a Transverse  Magnetic 
Field  29 

Table  2 Summary  of  Measurements  of  the  Resistance 
Change  of  #40  B & S Copper  Wire  in  the 
Magnetic  Field  30 

Figure  la,  lb  Variation  of  Electrical  Resistance  of 

#40  B & S Copper  Wire  in  the  Magnetic  Field  31 


■ 


ORIGIN  AND  SCOPE 

During  the  course  of  an  investigation  by  Professor  A.  P. 

Carman  on  the  resistance  of  a metallic  conductor  in  the  field  of 
a rotating  magnet,  question  arose  as  to  the  value  of  the  resistance 
change  caused  by  the  stationary  magnetic  field  alone.  A short 
search  through  the  literature  on  this  subject  showed  that  this  phe- 
nomenon, although  quite  well  known,  has  been  studied  quantitatively 
in  the  case  of  only  a few  elements,  particularly  iron,  nickel,  and 
bismuth.  For  the  nonmagnetic  metals  such  as  gold,  silver,  copper, 
and  platinum  the  results  of  comparatively  few  measurements  are  avail- 
able. The  present  work  deals  with  the  development  of  a method  for 
the  determination  of  resistance  change  in  both  transverse  and  longi- 
tudinal magnetic  fields  and  with  measurements  made  on  copper.  The 
experimental  arrangements  were  adapted  particularly  for  the  study  of 
such  metals  in  wire  form  subjected  to  magnetic!  fields  of  2 to  16 
kilogausses.  The  measurements  were  in  all  cases  made  at  room  tem- 
perature, about  21°C. 


' 


.. 


' 


. . 


- 


1 


- 


2 


II 

HISTORICAL  REVIEW  OF  EXPERIMENTAL  STUDY 

The  possibility  of  a change  in  electrical  resistance  result- 
ing from  the  action  of  a magnetic  field  was  perhaps  first  suggested 
by  the  experiment  of  Maggi  (1)  who  believed  that  he  had  established 
a change  in  the  thermal  conductivity  of  an  iron  disk  in  a magnetic 
field.  In  the  year  1824  both  Abraham  (2)  and  Fischer  (3)  reported 
experiments  on  the  electrical  conductivity  of  magnetized  iron. 

Their  results  were  conflicting  and  were  furthermore  of  little  weight 
since  they  used  friction  or  influence  machines  as  a source  of  cur- 
rent and  had  no  accurate  method  for  resistance  measurement.  Edlund 
(4),  in  1854,  was  probably  the  first  to  employ  a method  sufficiently 
sensitive  to  obtain  definite  results.  He  applied  a longitudinal 
magnetic  field  to  iron  wire  and  made  his  resistance  determinations 
with  a Wheatstone  net  work.  He  detected  no  change,  perhaps  because 
the  field  which  he  applied  was  not  sufficiently  strong. 

The  existance  and  magnitude  of  the  effect  were  finally  estab- 
lished beyond  doubt  in  185G  by  Professor  William  Thomson  (5),  later 
Lord  Kelvin.  He  worked  with  nickel  and  iron,  applying  both  longi- 
tudinal and  transverse  magnetic  fields.  The  most  significant 
advance  to  be  noted  in  his  experimental  arrangement  is  the  care 
in  securing  close  temperature  control.  Both  the  iron  and  the 
standard  resistance  were  surrounded  by  liquid  baths.  The  magni- 
tude of  the  change  in  resistance  was  found  to  be  about  l/3,000  of 
the  normal  resistance.  Also,  the  conductivity  was  greater  along 
than  across  the  lines  of  magnetization.  No  estimate  is  given  of 


. 


3 

the  strength  of  the  magnetic  field  applied. 

The  next  experiments  reported  are  those  of  Beetz  (6)  in  1866. 
His  results  were  of  little  quantitative  value  but  the  work  offers 
a suggestion  which  has  been  followed  by  later  investigators. 

Beetz  used  iron  wire  in  a longitudinal  field  and  measured  both  the 
change  in  length  and  the  change  in  resistance. 

Working  about  ten  years  later,  Adams  (7)  also  studied  iron. 

He  placed  bars  of  the  metal  inside  a solenoid,  thus  securing  longi- 
tudinal magnetization  and  found  that  the  resistance  change  was  pro- 
portional to  the  square  of  the  magnetizing  current,  or  that  the 
AR 

ratio  Tg  was  approximately  constant.  For  large  values  of  i,  how- 
ever, the  ratio  tended  to  decrease  in  value.  Auerbach  (8)  in  per- 
forming similar  experiments  measured  the  temperature  of  the  speci- 
men by  means  of  a thermocouple  to  determine  the  necessary  tempera- 
ture correction  and  also  measured  the  magnetic  moment  of  the  iron 
for  the  various  fields  applied.  He  found  that  the  change  in  resis- 
tance was  proportional  to  the  moment  of  magnetization  rather  than 

, AR 

to  the  field,  thus  explaining  the  drop  in  value  of  Adams’  ratio  “ 
for  large  values  of  i,  for  saturation  values  of  the  field. 

Goldhammer  (9)  reported  in  1887  and  1889  study  of  quite  an  ex- 
tensive series  of  metals,  including  bismuth,  nickel,  tellurium, 
antimony,  cobalt,  and  iron.  He  deposited  the  metals  electro lyti- 
cally  on  glass,  using  only  a thin  film.  One  of  the  chief  objects 
of  this  arrangement  v/as  the  avoidance  of  internal  stress  in  the 
metal  as  a result  of  magnetization.  Both  longitudinal  and  trans- 
verse fields  were  employed.  Goldhammer' s results  were  similar  to 
those  of  Adams  and  Auerbach;  R = A K2  Rc  , as  he  put  it,  A being  a 
constant  characteristic  of  the  metal  and  K its  magnetizing  factor. 


& 


' 


4 


In  the  study  of  later  progress  it  is  probably  best  to  take 
advantage  of  the  classification  used  by  Koenigsberger , who  has 
written  the  section  on  metallic  conduction  in  Graetz’  Handbuch 
der  Elektricit&t  und  des  Magnetismus.  The  matter  is  therefore 
divided  into  three  groups,  accordingly  as  it  pertains  to  material 
which  is  (1)  ferromagnetic,  (2)  strongly  diamagnetic  or  weakly  ferro- 
magnetic, (3)  paramagnetic  or  weakly  diamagnetic.  In  the  first 

v 

group  are  nickel,  iron,  and  cobalt;  in  the  second  are  bismuth,  an- 
timony, tellurium,  and  graphite;  in  the  third  gold,  silver,  copper, 
cadmium,  platinum,  and  palladium. 

In  the  case  of  ferromagnetic  materials  the  difference  between 
the  effect  of  a transverse  and  that  of  a longitudinal  field  is  most 
marked.  Iron  and  nickel  are  the  elements  which  have  received  the 
greatest  amount  of  attention.  There  is  some  discrepancy  betv/een 
results  obtained  by  different  experimenters  here,  particularly  for 
the  action  in  a transverse  field.  The  discrepancy  seems  to  be  due 
as  much  to  difference  in  the  nature  of  specimens  observed  as  to 
experimental  error.  The  results  of  most  investigators  indicate 
that  a longitudinal  field  causes  an  increase  in  resistance  and  that 
this  increase  in  resistance  approaches  a limiting  value  for  high 
fields.  In  the  transverse  field  the  resistance  first  rises  to  a 
maximum  and  then  decreases  to  a value  less  than  that  for  zero  field. 

Among  the  most  important  experiments  on  iron  in  a transverse 
magnetic  field  are  those  of  Grunmach  and  Weidert  (10),  d* Ago s tiro 
(11),  Alpheus  W.  Smith  (12),  and  Heaps  (13).  Grunmach  and  Weidert 
used  samples  of  pure  iron  wire  and  of  piano  wrire . In  every  case 
except  one  they  found  an  initial  increase  in  resistance  which 
reached  a maximum  in  a field  of  the  order  of  2 kilogausses.  A sub- 


J 


~ 


5 


sequent  decrease  in  the  higher  fields  reduced  the  resistance  below 
its  initial  value.  D’Agostino  used  both  wire  and  bands  of  iron. 

In  the  specimens  which  he  had  the  initial  increase  in  resistance 
did  not  appear,  the  change  being  from  the  beginning  a decrease. 

This  was  also  the  behavior  of  one  sample  observed  by  Grunmach  and 
Weidert.  Smith  and  Heaps  have  both  found  about  the  same  action 
that  Grunmach  and  Weidert  reported,  an  initial  increase  and  a sub- 
sequent decrease  to  a value  even  below  that  in  zero  field. 

Work  on  nickel  in  a transverse  field  has  been  carried  on  by 
Williams  (14),  Knott  (15),  and  by  Blake  (16)  in  addition  to  those 
mentioned  above  in  connection  with  measurements  on  iron.  Nickel 
also  shows  the  initial  increase  and  following  decrease.  The  data 
of  Blake,  which  are  the  most  accurate  yet  obtained,  show  that  in 
the  temperature  range  from  -190°C  to  186°C  the  decrease  is  much 
greater  than  the  temporary  increase. 

In  a longitudinal  field  the  resistance  of  nickel  and  of  iron 
increases,  rising  rapidly  to  a maximum.  There  is  no  subsequent  . 
drop  as  in  the  case  of  the  transverse  field.  In  the  few  cases 
where  a decrease  was  reported,  it  has  been  shown  that  this  was  the 
result  of  inaccurate  alignment  of  the  specimen  so  that  there  was  a 
transverse  component  of  magnetization  to  which  the  decrease  was 
due.  Among  the  best  experiments  here  are  those  of  Williams  (14), 
Blake  (IS),  Knott  (15),  Heaps  (13),  and  Alpheus  W.  Smith  (12). 

Cobalt  although  also  a member  of  this  group  has  been  subjected 
to  comparatively  little  study.  One  of  the  chief  difficulties  here 
lies  in  the  obtaining  of  a sample  of  a high  degree  of  purity.  The 
effect  of  a slight  impurity  on  the  electrical  conductivity  of  a 
metal  is  well  known.  On  such  an  electromagnetic  phenomenon  as  this 


- 

• 

. 

r . 

- 

• 

• 

‘ 

• 

* 

. 

. r It  ' 


! 


. 


6 

the  effect  of  impurities  is  even  more  disturbing.  Grunmach  and 
Weidert  (10)  found  that  cobalt  also  showed  the  behavior  character- 
istic of  ferromagnetic  elements,  the  decrease  in  the  transverse 
magnetic  field.  Their  results  indicated  a possibility  of  a slight 
initial  rise  but  did  not  confirm  it.  In  the  longitudinal  field  the 
resistance  of  cobalt  increases  similarly  to  that  of  iron  and  nickel. 

In  the  group  of  strongly  diamagnetic  and  weakly  ferromagnetic 
materials  bismuth  occupies  by  far  the  most  prominent  place.  In 
fact,  this  element  has  received  more  attention  than  any  other  in 
this  group  or  the  other  groups.  Bismuth  is  unique  in  the  magni- 
tude of  its  change  in  resistance  in  the  magnetic  field.  The  effect 
is  an  increase  in  both  the  longitudinal  and  the  transverse  fields. 
The  variation  of  the  change  with  temperature  is  also  unusually 
great.  The  work  of  Lennard  (18)  who  used  spirals,  measuring  the 
resistance  change  for  both  direct  and  alternating  currents,  is  par- 
ticularly important.  His  experiments  showed  that  the  resistance 
change  as  measured  by  alternating  current  is  different  from  that 
measured  by  direct  current.  This  difference  is  a function  of  the 
magnetic  field,  reversing  sign  at  about  6 kilogausses.  Among  the 
best  quantitative  work  on  bismuth  is  that  of  Henderson  (IS)  and 
Blake  (16).  Both  used  fields  well  above  30  kilogausses  and  made 
their  measurements  over  a considerable  temperature  range. 

Antimony',  tellurium  and  graphite  have  also  received  consider- 
able attention.  All  exhibit  an  increase  in  resistance  for  both 
the  transverse  and  the  longitudinal  field.  One  of  the  chief  facts 
that  renders  the  results  on  these  first  two  metals  interesting  is 
the  disparity  between  the  ratio  of  the  resistance  change  in  them  to 
that  in  bismuth  and  the  corresponding  relation  for  the  Hall  effect. 


f 


" : ‘ 


- 


» 0 £Mtj  a , 


7 


since  the  change  in  resistance  is  sometimes  viewed  as  a manifesta- 
tion of  the  Hall  effect.  Work  on  graphite  has  been  suggested 
partly  by  its  negative  temperature  coefficient  of  resistance  and 
partly  by  the  possibility  of  investigating  the  effect  of  crystal 
structure.  In  this  connection  the  work  of  de  Haas  (20)  on  antimony 
and  that  of  Roberts  (21)  on  graphite  is  important. 

i 

The  paramagnetic  and  weakly  diamagnetic  materials,  nearly  all 
of  them  good  conductors,  show  a much  smaller  change  in  resistance 
in  the  magnetic  field  than  do  the  elements  of  either  of  the  other 
groups.  In  every  result  that  has  been  confirmed,  the  change  is  an 
increase,  usually  slightly  greater  in  the  transverse  than  in  the 
longitudinal  field.  The  generalization  of  Goldhammer  that  the  dia- 
magnetic elements  show  a greater  resistance  alteration  than  do  the 
paramagnetic  elements  holds  fairly  well.  For  any  one  metal,  vari- 
ations are  dependent  upon  the  magnetic  susceptibility  of  the  sample 
used.  D'Agostino  (11)  was  the  first  to  make  fairly  accurate  mea- 
surements on  a large  number  of  substances . His  work  included  cadmi- 
um, zinc,  gold,  palladium,  mercury,  silver,  copper,. and  platinum  as 
well  as  invar,  manganin,  and  german  silver.  For  platinum  and  the 
three  alloys  he  reported  a decrease.  This  has  not  been  confirmed. 

In  gold,  silver,  and  copper,  the  change  was  too  slight  to  be  deter- 
mined by  his  method.  Later-  work  by  Grunmach  and  Weidert  (10)  and 
by  Heaps  (13)  indicates  that  these  three  metals  as  well  as  platinum 
all  increase  slightly  in  resistance.  Heaps’  measurements  are  valu- 
able particularly  in  the  comparison  offered  of  the  transverse  and 
the  longitudinal  effects.  The  work  of  d'Agostino  and  of  Grunmach 
and  Weidert  was  confined  to  changes  in  the  transverse  field.  Kam- 
merlingh  Onnes  and  Hof  (22),  and  Beckman  (23)  have  carried  out  a 


. 


- 


- 


- 


- 


- 


8 

large  number  of  measurements  with  such  metals  at  the  very  low  tem- 
peratures of  from  2°K  to  25°K. 

In  regard  to  liquids  the  results  are  not  yet  beyond  question. 
Measurements  on  mercury  and  molten  bismuth  have  been  made  by  Drude 
and  Nernst  (24)  and  later  by  Berndt  (25).  The  first  investigators 
found  a slight  increase  in  resistance  of  the  order  of  0.2 % for  both 
bismuth  and  mercury.  However,  the  effect  in  bismuth  was  much 
smaller  than  that  for  the  same  sample  when  solid  and  that  in  mercury 
varied  greatly  with  the  current  through  the  bridge.  It  was  suggest- 
ed that  this  change  in  resistance  was  not  of  the  same  nature  as  that 
found  in  solid  conductors  but  might  be  the  result  of  electrodynamic 
action  on  the  fluid  conductor.  Des  Coudres  (26)  has  suggested  that 
the  magnetic  field  may  cause  turbulent  motion  in  the  fluid  if  it  is 
contained  in  a tube  having  bends,  as  was  the  case  here.  The  result- 
ing energy  consumption  would  be  manifested  as  an  increase  in  resis- 
tance. The  pinch  effect  noted  by  Hering  (27)  would  result  in  an 
increase  in  resistance,  but  it  is  doubtful  whether  it  would  be  of 
sufficient  magnitude  to  be  effective  at  such  lew  current  densities 
as  are  used  in  measurement.  Berndt  (25),  in  connection  with  mea- 
surements on  a number  of  electrolytes,  observed  also  mercury  and 
molten  bismuth,  the  latter  however  being  75  0 above  the  temperature 
at  which  Drude  and  Herns t (24)  worked.  He  too  employed  capillary 
tubes  but  of  much  smaller  diameter  than  those  used  by  Drude  and 
Nernst.  The  object  in  reducing  the  diameter  was  to  prevent  as  far 
as  possible  turbulent  motion  of  the  fluid.  In  a transverse  field 
of  3 kilogausses  the  resistance  of  mercury  remained  constant  to  less 
than  l/2, COO  %,  so  Berndt  reported.  In  a longitudinal  field  of  1 
kilogauss  he  gives  l/20,000  % as  the  upper  limit  of  any  change. 


- 


’ 


9 

None  was  actually  detected  In  either  case.  To  bismuth  only  the 
transverse  field  of  3 kilogausses  was  applied.  The  upper  limit  giv- 
en for  any  possible  change  in  resistance  here  is  l/660  %.  Berndt’s 
work  appears  to  have  been  very  carefully  done  and  in  the  absence  of 
better  data  his  conclusion  that  liquid  metallic  conductors  show  no 
resistance  change,  within  the  limits  indicated,  must  be  accepted. 

It  should  be  added  that  his  measurements  on  electrolytes,  including 
solutions  of  iron,  nickel,  bismuth,  and  copper  compounds  all  indi- 
cated that  any  resistance  change  occurring  must  be  less  than  l/250  %> 
Transverse  fields  of  3 kilogausses  and  longitudinal  fields  of  1 
kilogauss  were  applied.  In  the  work  wTith  electrolytes  alternating 
current  was  used.  The  resistance  change  of  copper  in  a field  of  10 
kilogausses  is  about  0.003$,  so  that  if  that  of  electrolytes  varied 
as  much  as  is  the  case  with  copper,  Berndt  would  not  have  detected 
it . 

In  general,  the  three  groups  of  metals  are  quite  distinct.  The 
ferromagnetic  group  is  characterized  by  the  decrease  in  resistance 
in  moderate  and  high  transverse  fields  and  by  the  limitation  of  re- 
sistance increase  in  the  longitudinal  field.  Except  for  bismuth, 
the  strongly  diamagnetic  and  weakly  ferromagnetic  materials  exhibit 
a smaller  change  in  resistance  and  do  not  show  the  great  decrease 
in  resistance  in  strong  transverse  fields.  The  paramagnetic  and 
weakly  diamagnetic  elements  show  the  least  change  in  resistance. 

The  difference  in  longitudinal  and  transverse  effects  is  less  in 
these  metals  too.  For  the  ferromagnetic  elements  the  longitudinal 
resistance  effect  is  proportional  to  the  square  of  the  magnetiza- 
tion. For  the  second  group,  the  square  relation  is  not  so  satisfac- 
tory. The  metals  of  the  last  group  exhibit  a change  in  both  trans- 


- 


* 


* 


. 


■ 


10 


verse  and  longitudinal  fields  which,  for  the  smaller  field  values, 
is  fairly  well  represented  as 

AR  p 

T = A H • 

For  large  values  of  H the  correspondence  between  this  equation  and 
experimental  results  is  not  so  good.  In  fact,  the  variation  there 
seems  to  be  more  nearly  as  the  first  power  of  H. 


11 

III 

THEORETICAL  TREATMENTS 

Present  theories  of  metallic  conduction  hardly  explain  in  a 
convincing  manner  the  variation  of  resistance  with  temperature  and 
pressure  over  the  range  covered  by  experimental  data.  A satisfac- 
tory theoretical  explanation  of  the  resistance  changes  here  dis- 
cussed is  therefore  hardly  to  be  expected. 

Most  theories  now  supported  place  the  burden  of  conduction  on 
the  electron.  Corbino  (28)  and  his  co-workers  in  Italy  have  re- 
tained the  older  idea  of  two  types  of  ions,  one  bearing  a positive 
charge  and  the  other  a negative.  Mathematically  their  theory  is 
much  like  those  more  widely  accepted.  With  the  two  carriers,  how- 
ever, they  have  the  advantage  of  a larger  number  of  equations  and 
arbitrary  constants  so  that  the  theoretical  deductions  may  be  made 
to  conform  to  more  diverse  experimental  results.  For  instance,  the 
reversal  of  sign  of  the  Hall  effect  in  some  metals  may  be  explained. 
Aside  from  the  initial  postulate  of  both  positive  and  negative  car- 
riers, the  assumptions  made  in  developing  this  theory  are  practical- 
ly the  same  as  those  for  the  more  widely  held  electron  theories,  and 
on  the  whole,  experimental  evidence  seems  to  point  more  clearly  to 
the  single  negative  carrier. 

The  pioneer  attempt  to  give  an  explanation  of  the  increase  in 
resistance  in  a magnetic  field  was  that  of  Sir  J.  J.  Thomson  (29) 
in  1900.  He  assumed  that  in  the  normal  state  electrons  were  moving 
freely  about  at  random  writhin  the  metal,  as  do  the  molecules  of  a 
gas  in  a container.  When  an  electric  force  was  applied,  there  was 
set  up  a drift  which  constituted  the  current.  The  resistance  is 


. 


■ 


12 


supposed  to  be  the  result  of  collisions  between  the  electrons  and 
the  molecules  of  the  metal.  In  the  magnetic  field  the  path  of  a 
moving  electron  is  altered  and  as  a result  of  this  the  resistance 
changes.  In  order  to  get  the  right  sign  for  the  change  it  is  ne- 
cessary to  assume  that  the  collisions  between  electrons  and  atoms 
are  greatly  influenced  by  the  charges  borne  by  the  electrons.  The 
expression  given  is 


where  T is  the  mean  free  period  of  an  electron.  Such  an  explanation 
is  evidently  inadequate;  no  indication  is  given  of  a variation  of 
the  resistance  change  in  ferromagnetic  materials  from  that  in  para- 
magnetic materials  or  of  the  difference  between  solid  and  liquid 
conductors . 

Lorentz  assumed  that  the  collisions  between  electrons  and 
atoms  were  like  those  between  hard,  elastic  spheres,  as  in  the  ki- 
netic theory  of  gases,  and  was  able  to  work  out  the  explanation  of 
some  thermoelectric  phenomena.  E.  P.  Adams  (30)  has  extended  this 
line  of  thought  by  applying  it  to  J.  J.  Thomson's  consideration  of 
resistance  change.  Another  modification  made  by  Adams  is  that  he 
assumes  not  only  the  change  in  path  of  the  moving  electron  but 
also  a change  in  the  molecular  configuration  of  the  metal  which  be- 
comes an  additional  factor  operating  to  change  the  resistance.  His 
expression  for  the  resistance  change  in  a transverse  field  is  then 


The  sign  of  the  effect  -will  evidently  depend  on  the  relative  magni- 


' 


fl*.  k 


tude  of  the  change  in  free  time  resulting  from  alteration  in  molec- 
ular arrangement.  Using  Grunmach  and  Weidert’s  data  (10),  Adams 


In  this  case,  however,  AT  is  more  complex.  The  alteration  in  molec- 
ular configuration  is  effective  as  in  the  transverse  field.  Besides 
this,  the  spiral  path  of  a moving  electron  about  the  lines  of  mag- 
netization also  influences  T.  According  to  Adams’  development  the 
difference  between  the  transverse  and  the  longitudinal  effect  in  an 
isotropic  medium  should  be  given  by  the  equation 


Noting  that  in  the  paramagnetic  and  in  many  diamagnetic  ele- 
ments the  difference  between  the  transverse  and  longitudinal  effects 
is  very  small,  C.  W.  Heaps  (13)  has  presented  still  another  modifi- 
cation of  the  theory  to  make  it  accord  with  this  fact.  In  so  doing 
he  has  employed  and  extended  somewhat  the  equations  given  by  Town- 
send (31)  for  the  drift  of  electrons  under  the  action  of  mutually 
perpendicular  electric  and  magnetic  fields.  Assuming  the  current 
to  flow  along  one  axis  of  the  coordinate  system,  say,  the  x axis, 
a magnetic  field  parallel  to  the  z axis  will  result  in  the  building 
up  of  an  electric  field  parallel  to  the  y axis.  This  potential 
difference  along  the  y axis  is  then  the  Hall  effect;  Townsend  had 
ignored  it  in  his  consideration  of  the  problem,  being  interested 
chiefly  in  the  current  flow  itself.  Heaps  included  in  his  consid- 
eration the  potential  thus  built  up  along  the  y axis  and  its  effect 


calculated  T to  be  about  3*10“^  second  and  about  2.5*10”'J 
For  the  longitudinal  field  his  analysis  gives 


AR  _ AT 

R T 


■ 

. 


- 


« 


■ 


14 


on  the  motion  parallel  to  the  x axis.  With  this  change,  the  devel- 
opment indicates  that  the  electron  flow  is  not  affected  by  the  mag- 
netic field;  that  is,  the  action  of  the  magnetic  field  on  the  mov- 
ing electrons  does  not  result  in  a change  of  resistance.  The  ex- 
pression for  the  current  with  or  with  out  the  field  is  then 


where  n is  the  number  of  electrons  per  unit  volume.  Changes  in  re- 
sistance must  therefore  be  the  result  of  variations  in  Ex,  T,  or  n 
caused  by  the  field  applied. 

Experiments  by  Roberts  (21)  on  crystalline  graphite,  de  Haas 
(20)  on  antimony,  and  Heaps  (13)  on  bismuth,  graphite,  and  cadmium 
indicate  that  the  relative  directions  of  the  magnetic  field  and  the 
current  have  little  or  no  effect  on  the  resistance  change.  The 
effect  of  the  field  is  therefore  probably  confined  to  changes  in  T 
and  in  n.  The  general  expression  given  for  the  resistance  change 
in  the  magnetic  field  then  becomes 

AR  _ n0T0  _ 

R nT  1 

where  n0  and  T0  are  the  values  for  zero  magnetic  field.  Both  n and 
T are  supposed  to  be  functions  of  unknown  form  of  H. 

The  various  theories  advanced  offer  none  too  good  an  oppor- 
tunity for  experimental  test.  The  results  of  Thomson  (29)  and  Adams 
(30)  as  well  as  those  of  Gans  (32)  and  Livens  (33)  all  indicate 

that  ~ should  be  proportional  to  the  factor  (Jj)  ^ T2  H2  or  to  the 
e 2 i 2 

factor (“)  (^)  H2,  substituting  l/v  for  T,  where  1 is  the  mean 

AR 

free  path  and  v the  mean  velocity.  From  this,  — should  be  propor- 


■ 


. 


15 

tional  to  the  square  of  the  field.  This  might  have  been  antici- 
pated at  once  from  the  symmetry  of  the  action,  since  reversal  of 
current  or  field  has  no  effect. 

Another  possibility  of  experimental  test  appears  in  the  same 

factor.  The  mean  free  path,  1,  is  proportional  inversely  to  the 

A>H 

absolute  temperature,  0.  As  a result,  — should  be  proportional  to 

ft 

e-» 

Experimental  results  show  with  a fair  approximation  a variation 
in  resistance  according  to  the  law 

Y - A H2  . 

The  variation  of  resistance  change  with  temperature  does  not  follow 
the  theoretical  prediction. 


' 


- 

■ 


. 


16 

IV 

SUGGESTIVE  EXPERIMENTS,  THEIR  BEARING  ON  THE  THEORY 

It  is  thought  worth  while  to  mention  briefly  a few  experiments 
which  are  of  particular  value  for  the  suggestions  they  offer  with 
respect  to  further  investigation  or  for  their  bearing  on  the  theo- 
retical explanations  of  the  resistance  effect. 

The  suggestion  that  resistance  change  for  paramagnetic  materi- 
als is  proportional  to  the  square  of  the  field  strength  or  that 

f 

was  tested  carefully  by  Heaps  (13)  in  observations  on  gold,  zinc, 
cadmium,  bismuth,  tellurium,  and  lead  sulfide  in  both  transverse 
and  longitudinal  fields.  It  has  been  stated  above  that  the  equation 
holds  quite  well  for  low  values  of  H,  for  high  values  the  change  is 
less  than  the  equation  would  indicate. 

Opportunity  to  test  the  relation 

AR  _3 

T*  B « 

is  given  by  the  data  of  Blake  on  bismuth  and  nickel  at  temperatures 
ranging  from  -190°C  to  186°C  and  by  the  large  amount  of  data  taken 
at  helium  temperatures  by  Onnes  and  Hof  (22)  and  by  Beckman  (23). 

The  agreement  with  experimental  results  is  not  good  over  a large  or 
over  a small  temperature  range. 

The  effect  of  crystal  structure  and  of  the  orientation  of  the 
crystal  in  the  magnetic  field  was  studied  in  considerable  detail  by 
van  Everdingen  (34)  before  1900.  This  line  of  work  has  been  con- 


* 

SX 

' 


- 


17 

tinued  also  by  other  Dutch  investigators,  among  whom  de  Haas  (20) 
has  been  mentioned.  The  resistance  of  bismuth  crystals  is  normally 
different  in  two  different  directions  and  may  be  represented  by  an 
ellipsoid  of  revolution.  In  the  magnetic  field  three  unequal  axes 
are  necessary  to  show  the  resistance  characteristics.  Instead  of 
the  simple  relation 

— = A 


R 


these  expe  rimenters  have  found  that  the  effect  for,  say,  crystalline 
bismuth,  should  be  given  as  a function  of  the  components  of  the 
field  parallel  to  the  various  crystal  axes.  The  equation  is  there- 
fore written 


AR 

R 


nll  (aH)2+  nl2  (bH)2+  nl3  ( °H) 


where  a,  b,  and  c are  direction  cosines  and  n-^,  n-^g,  and  n-^  char- 
acteristic constants.  This  form  has  been  used  by  van  Everdingen 
and  more  recently  by  Borelius  and  Lindh  (35).  The  experiments  of 
de  Haas  (20)  on  antimony,  Roberts  (21)  on  graphite,  and  Heaps  (13) 
on  bismuth,  graphite,  and  cadmium  all  reenforce  the  conclusion  that 
the  crystal  structure  of  the  conductor  plays  a very  important  part 
in  resistance  changes. 

In  connection  with  the  work  on  the  effect  of  crystal  structure 
it  is  perhaps  well  to  recall  the  work  done  on  liquid  conductors.  To 
the  limit  of  accuracy  of  the  experiment,  and  this  was  quite  good,  it 
indicated  that  in  all  these  substances  lacking  crystalline  charac- 
teristics the  magnetic  field  produced  no  change  in  resistance. 

A very  interesting  set  of  data  is  that  presented  recently  by 
Alpheus  W.  Smith  (12).  He  measured  the  change  of  thermoelectric 


18 


force  in  the  magnetic  field  for  a wire  subjected  to  tension  of  vari- 
ous magnitudes.  Data  taken  by  other  investigators  for  similar  ob- 
servations with  respect  to  changes  in  resistance  and  changes  in 
length  are  also  given.  The  similarity  of  the  variation  of  all 
three  is  striking.  Heaps  (13)  had  previously  made  simultaneous  mea- 
surements of  resistance  and  length  changes  for  iron  and  nickel  and 
pointed  out  the  direct  relation  between  the  two  effects. 

The  work  of  B.  C.  Knott  (15)  on  nickel  subjected  to  the  com- 
bined action  of  transverse  and  longitudinal  fields,  one  of  which 
varies  periodically  has  been  very  carefully  done.  The  immediate 
value  of  his  results  seems  to  be  diminished  rather  than  increased  by 
the  complexity  of  the  action. 


i 


19 


V 

EXPERIMENTAL  WORK  HERE 

The  object  of  the  experimental  investigation  was,  in  brief, 
the  determination  of  both  the  longitudinal  and  the  transverse  re- 
sistance changes  in  the  magnetic  field  exhibited  by  metals  such  as 
copper;  gold,  and  silver.  The  first  problem,  therefore,  was  the 
choice  of  a method  for  the  accurate  measurement  of  small  resistance 
increments.  The  method  employed  was  essentially  that  of  the  bolom- 
eter. A balanced  Wheatstone  bridge  is  used  and  the  resistance 
changes  may  be  measured  either  by  the  resulting  galvanometer  deflec- 
tions or  by  changes  made  in  one  arm  of  the  bridge  to  maintain  the 
balance.  The  deflection  method  is  much  more  rapid  than  the  other 
and  is  sufficiently  accurate.  In  order  to  employ  this  method  the 
relation  between  galvanometer  deflections  and  the  resistance 
changes  which  cause  them  must  be  known.  This  information  was  ob- 
tained by  observing  the  change  in  deflection  when  a one  ohm  resis- 
tance in  series  with  the  sample  and  in  the  same  arm  of  the  bridge 
was  shunted  by  a resistance  of  1000  ohms,  thus  giving  AR  ="0 .001 
ohm,  very  nearly. 

The  maximum  sensitiveness  of  the  bolometer  is  secured  when  the 
four  arms  are  equal  and  each  is  twice  the  resistance  of  the  galva- 
nometer. As  the  result  of  limitation  of  space  available  for  the 
specimen  under  investigation  this  condition  was  not  fulfilled.  The 
four  arms  were  approximately  equal  and  each  was  a little  less  than 
the  galvanometer  resistance. 

The  material  on  which  the  observations  were  made  was  #40  B & S 


■ 


20 

copper*  wire,  double  silk  covered.  It  had  been  purchased  some  years 
before  for  the  construction  of  fine  galvanometers  and  therefore  is 
believed  to  be  quite  pure.  This  wire  was  wound  around  thin  strips 
of  mica  about  6.2  mm  wide  and  7.6  cm  long  so  as  to  be  in  the  form 
of  a rectangular  spiral  with  one  side  6.2  mm  long  and  the  other 
approximately  0.2  mm.  Of  the  7.6  cm  length  only  about  1.8  cm  was 
occupied  by  this  winding,  since  the  field  available  was  circular  in 
shape  and  only  2.5  cm  in  diameter. 

Five  such  units  fastened  firmly  together  formed  a compact  re- 
sistance of  about  20  ohms.  The  connections  were  of  course  soldered 
here  and  at  all  other  points  possible.  The  extra  length  of  the 
mica  strips  was  quite  convenient  in  handling  the  windings.  In  order 
to  secure  accurate  alignment  in  the  magnetic  field  this  group  of 
resistances  was  fastened  on  the  shaft  of  a T-shaped  piece  of  sheet 
brass.  The  plane  of  the  mica  strips  was  parallel  to  that  of  the 
shaft.  Consequently,  the  longer  dimension  of  the  wire  was  parallel 
to  the  cross  bar  of  the  T and  no  difficulty  was  experienced  in  the 
adjustment  either  for  longitudinal  or  transverse  fields.  Chiefly 
for  the  sake  of  thermal  insulation,  the  resistance  unit  so  prepared 
was  placed  in  a box  8 mm  square  and  about  5 cm  high  made  of  very 
thin  sheet  copper.  The  upper  part  of  the  shaft  and  the  cross  bar 
of  the  T of  course  projected  outside.  The  extra  space  within  the 
box  was  filled  with  paraffin  poured  in  wliile  hot  and  allowed  to 
cool  so  that  the  wire  was  held  firmly  in  place.  Leads  of  #30  Ad- 
vance having  a negligible  temperature  coefficient  were  brought  out. 

In  an  early  series  of  measurements  made  on  copper  wound  on  a 
hard  rubber  spool  and  placed  directly  between  the  circular  pole- 
pieces  for  determination  of  the  transverse  effect,  it  was  found  that 


. 


. 

_ ' ■ 


. 


. 


■ 


21 

the  temperature  variation  of  the  sample  was  fairly  regular.  By 
taking  deflection  readings  at  intervals  of,  say,  20  seconds,  with 
the  magnetic  field  alternately  on  and  off  the  increase  in  resistance 
due  to  temperature  rise  could  be  determined  and  correction  made 
accordingly.  Plotting  deflection  as  ordinate  and  time  as  abscissa, 
two  approximately  parallel  curves  appeared,  one  for  the  resistance 
in  the  magnetic  field  and  the  other  for  the  resistance  in  zero  field. 
The  slope  of  each  curve  is  determined  by  the  rate  of  change  of  tem- 
perature. The  mean  distance  between  the  two  curves,  measured  par- 
allel to  the  axis  of  ordinates,  gives  a measure  of  the  resistance 
change  caused  by  the  magnetic  field  alone.  Actually  it  is  not 
necessary  to  plot  the  curves.  The  mean  difference  between  succes- 
sive deflections  gives  the  value  desired.  This  is  the  method  used 
by  Grunmach  and  Weidert  (1C)  in  their  work  on  the  transverse  effect. 
Proceeding  in  this  manner,  a fairly  consistent  set  of  data  on  copper 
was  obtained. 

The  wire  had  been  wound  in  bifilar  fashion  on  the  spool  but 
there  was  still  quite  an  inductive  kick  so  that  for  strong  fields 
the  time  between  readings  was  increased  to  30  seconds  to  allow  the 
galvanometer  coil  to  return  to  its  normal  position.  When  the  copper 
specimen  was  replaced  by  one  of  platinum,  wound  similarly  on  a hard 
rubber  spool,  the  difference  between  measurements  made  with  a time 
interval  of  30  seconds  and  those  with  an  interval  of  15  seconds  be- 
came very  great,  amounting  to  as  much  as  50^.  An  extended  series 
of  observations  showed  that  this  discrepancy  was  the  result  of  the 
irregular  rate  of  temperature  change  of  the  sample . With  the  mag- 
net energized  periodically  the  heat  supply  was  of  course  periodic 
and  it  was  as  a result  of  this  that  the  large  difference  between 


JAJ 


- 


22 


measurements  for  different  time  intervals  appeared. 

In  order  to  correct  this,  arrangements  were  made  for  a constant 
flow  of  kerosene  through  the  space  between  the  resistance  and  the 
pole  pieces,  the  resistance  now  being  wound  on  mica  and  enclosed  in 
a copper  box  as  described.  With  this  arrangement  the  heat  from  the 
magnet  was  taken  up  by  the  liquid  and  carried  away.  Preliminary 
trials  showed  that  fluctuations  in  the  temperature  of  the  oil  might 
easily  cause  as  much  trouble  as  the  irregular  rate  of  change  it  was 
desired  to  avoid.  As  a partial  correction  for  this,  the  oil  was 
passed  through  a spiral  of  small  brass  tubing  immersed  in  a large 
tub  of  water  at  room  temperature . Slow  changes  in  the  temperature 
of  the  sample  could  hardly  be  prevented  but  they  were  made  quite 
regular.  Difficulty  with  this  gradual  change  was  greatly  reduced 
by  the  use  of  a second  resistance  of  copper  in  an  arm  of  the  bridge 
adjacent  to  the  sample.  This  second  copper  resistance  also  was 
placed  in  the  bath  of  flowring  oil.  The  other  two  arms  of  the  bridge 
then  were  made  up  of  two  Otto  Wolff  resistance  boxes  with  a slide 
wire  between  them  for  convenience  in  balancing. 

In  preparing  for  a series  of  observations  great  care  was  taken 
that  the  many  disturbing  influences  affecting  the  resistance  of  the 
coil  might  come  to  an  equilibrium  before  measurements  were  begun. 

To  this  end  the  oil  flow  was  started  at  least  30  minutes  before  the 
first  reading.  The  bridge  current  too  was  allowed  to  pass  for  some 
time  before  beginning  the  run  and  continuously  during  its  course. 

The  magnet  was  energized  at  the  regular  time  intervals  for  several 
periods  before  any  measurements  were  made.  The  galvanometer  circuit 
was  closed  continuously  so  that  no  difficulty  with  thermal  electro- 
motive forces  in  it  was  experienced.  During  the  time  the  current 


, • 


■ 


' 


23 


through  the  magnet  was  changing,  about  5 seconds,  the  galvanometer 
leads  were  short  circuited  by  a copper-contact  key  to  prevent  large 
deflections  resulting  from  the  current  induced. 

With  the  preliminaries  finished,  the  procedure  was  quite 
simple,  consisting  only  of  deflection  readings  from  the  galvanom- 
eter at  20  second  intervals,  with  the  field  on  and  off  for  alternate 
periods  of  20  seconds  beginning  and  ending  immediately  after  a read- 
ing. The  sensitiveness  was  determined  before  and  after  such  a run 
by  a series  of  observations  of  the  change  in  deflection  resulting 
from  a change  of  0.001  ohm  in  the  X branch. 

In  Table  1 there  are  given  two  typical  sets  of  observations, 
the  first  for  the  determination  of  sensitiveness  and  the  s econd  for 
measurement  of  the  change  in  a field  of  about  11  kilogausses.  The 
first  column,  D,  gives  the  scale  reading;  the  second,  AD,  is  the 
difference  between  one  reading  and  that  preceding  it;  and  the  third, 
Aq,  is  the  difference  of  AD  from  its  mean.  Using  the  sum  of  the 
values  of  A?  the  probable  error  in  the  mean  value  of  AD  is  calcu- 
lated (36).  Variations  in  the  value  of  AD  are  the  result  mainly  of 
small  rather  rapid  changes  in  temperature  of  the  specimen.  These 
appear  to  be  wholly  irregular  and  so  their  effect  can  be  eliminated 
by  making  a number  of  observations  and  taking  the  mean.  For  values 
of -AD  greater  than  the  variation  this  is  satisfactory. 

A summary  of  the  data  taken  on  the  #40  copper  is  given  in 

AR 

Table  2.  The  last  column  in  each  case  gives  the  value  of  — - (=  A) 

RH^ 

which  should  be  approximately  constant  if  the  equation 

AR  p 

— = A H2 

is  to  represent  the  variation  of  resistance.  The  agreement  for  the 


- 


24 

case  of  the  transverse  field  is  considerably  better  than  that  for 
the  longitudinal  field.  In  both  cases  there  seems  to  be  a definite 
change  in  the  value  of  A as  the  field  increases.  Study  of  other 
specimens  will  be  required,  however,  before  it  can  be  stated  whether 
this  is  actually  the  case  and  to  determine  the  character  of  the 
variation  if  it  actually  exists.  The  mean  values  for  the  constants 
are 

Ax  = 2.40-KT7  At  = 2.86-10”7. 

These  values  are  for  the  field  strength  in  kilogausses.  Using  the 

_ i 3 o 

gauss  as  the  unit  the  factor  is  1C  instead  of  10  . 

A slight  correction  might  be  applied  to  these  values  because  of 
the  fact  that  the  wire  was  in  the  form  of  a rectangle  and  the  mea- 
surements were  made  with  the  longer  side  parallel  or  perpendicular 
to  the  lines  of  force.  However,  the  ratio  of  the  longer  to  the 
shorter  side  was  52:1  and  as  the  difference  bet?feen  the  two  con- 
stants is  small,  the  correction  is  less  than  the  experimental  error. 


_ 


25 


VI 

DISCUSSION 

In  continuing  the  experimental  investigation  measurements 
should  he  made  on  other  samples  of  copper,  as  well  as  on  gold,  sil- 
ver, platinum,  tungsten,  and  other  metals.  If  the  results  of  such 
further  measurements  establish  a change  in  the  value  of  A in  the 


equation 


AR 

R 


= A H‘ 


as  H increases,  it  may  be  well  to  divide  the  measurements  into  two 
groups,  the  first  covering  the  lower  range  of  values  of  H up  to  10 
or  12  kilogausses  and  the  second  range  for  values  of  H up  to  about 
50  kilogausses.  This  arrangement  of  the  work  would  permit  of  great- 
er accuracy  at  both  extremes  and  would  lessen  the  difficulties  met 
in  securing  the  necessary  temperature  control. 

It  has  been  suggested  that  the  crystal  structure  influences 
greatly  the  resistance  change.  A sample  in  the  form  of  wire,  as  a 
result  of  the  drawing  process,  would  not  be  expected  to  be  strictly 
isotropic.  Some  indication  of  the  effect  of  the  structure  might  be 
gathered  from  observations  on  films  formed  by  electrodeposition  and 
films  formed  by  sputtering  in  a vacuum.  The  latter  would  be  par- 
ticularly interesting  since  it  has  been  fairly  well  established 
that  when  such  a film  is  first  formed,  there  is  no  crystalline 
structure.  Perhaps  even  more  important  would  be  a repetition  of 
Berndt's  experiments  on  mercury,  using  fields  of  10  kilogausses  or 
more . 


- 


. 


26 


The  study  of  bismuth  or  the  ferromagnetic  elements  is  equally 
important  but  is  better  treated  as  a separate  field  of  investigation. 

This  discussion  would  be  incomplete  without  full  acknowledge- 
ment of  the  interest  and  aid  of  Professor  A.  P.  Carman  who  has 
directed  the  work. 


27 


BIBLIOGRAPHY 


(1)  Maggi,  Archiv  des  Sci.  Phys . et  Nat.  v.  14,  p . 132 

(2)  Abraham,  Archiv  f.  d.  gesammte  Naturlehre  (Kastner)  III,  426 

(3)  Fischer,  " " " " " III,  421 

(4)  Edlund,  Ann.  d.  Phys.  u.  Chemie  169,  315,  1854 

(5)  W.  Thomson,  Phil.  Trans.  146,  649,  1856 

(6)  Beetz,  Pogg.  Ann.  128,  193,  1866 

(7)  Adams,  Proc . Roy.  Soc . 23,  533,  1874-5 

Phil.  Mag.  (5)  1,  153,  1876 

(8)  Auerbach,  Wied.  Ann.  5,  289,  1878 

(9)  Goldhammer,  Wied.  Ann.  31,  360,  1887 

Wied.  Ann.  36,  807,  1889 

(10)  Grunmach  and  Weidert , Ann.  Phys.  22,  141,  1907 

(11)  d'Agostino,  Rend.  Accad.  Lincei  8,  531,  1908 

(12)  Alpheus  W.  Smith,  Phys . Rev.  19,  285,  1922 

(13)  Heaps,  Phil.  Mag.  22,  900,  1911 

Phil.  Mag.  24,  813,  1912 
Phys.  Rev.  6,  34,  1915 
" " 10,  366,  1917 

" " 19,  7,  1922 

(14)  Williams,  Phil.  Mag.  4,  430,  1902 

Phil.  Mag.  6,  683,  1903 
" " 9,  77,  1905 

(15)  Knott,  Edin.  Phil.  Soc.  Proe . 33,  200,  1913 

Edin.  Phil.  Soc.  Trans.  61,  39,  1904 

(16)  Blake,  Ann.  Phys.  28,  449,  1909 

(17)  Hurion,  C.  R.  100,  348,  1885 

(18)  Lermard,  Wied.  Ann.  39,  619,  1890 

(19)  Henderson,  Phil.  Mag.  38,  488,  1894 

(20)  de  Haas,  Konink.  Akad . Wetensch,  Amsterdam  16,  1110,  1914 

(21)  Roberts,  Ann.  d.  Phys.  40,  467,  1913 

(22)  K.  Onnes  and  Hof,  Comm.  Leiden  Nr.  142,  1914 

Akad.  Wet.  Amsterdam,  February  1914 
Versl.  Akad.  Wet.  Amsterdam  23,  493,  1914 
(Onnes  and  Beckman)  Comm.  Leiden  Nr.  129  a,  c;  130  a,  c; 
132  a,  b,  c,  d;  1912 

(23)  Beckman,  Comm.  Leiden.  Lab.  Suppl.  40,  Juni  1915 

(24)  Drude  and  Nernst,  Wied.  Ann.  42,  568,  1891 

(25)  Berndt,  Ann.  Phys.  23,  932,  1907;  Journ.  Phys.  7,  221,  1908 

(26)  Des  Coudres,  Berl . Phys.  Gs . Vh.  10,  50,  1891 

(27)  Hering,  (Northrup)  Phys.  Rev.  24,  476,  1907 

(28)  Corbino,  Nuovo  Cimento  (6)  16,  185,  1918 

(Trabacchi)  Nuovo  Cimento  (6)  12,  177,  1916 
(Trabacchi)  Atti.  Accad.  Lincei  18,  137,  1919 
(Freda)  Nuovo  Cimento  (6)  12,  177,  1916 

(29)  J.  J.  Thomson,  Rapp,  Congr.  intern.  Physique  3,  138,  1900 

(30)  E.  P.  Adams,  Phys.  Rev.  24,  428,  1907 

(31)  Townsend,  Electricity  in  Gases  (Oxford,  1915)  p.  100 

(32)  Gans,  Ann.  Phys.  20,  293,  1906. 

(33)  Livens,  Phil.  Mag.  30,  256,  1915 

(34)  van  Everdingen,  Archives  Neerlandaises  4,  371,  1901 

Archives  Neerlandaises  5,  453,  1901 

" " 6,  294,  1901 


28 

(35)  Borelius  and  Lindh,  Ann.  Phys . 53,  97,  1917 

(36)  Goodwin,  Precision  of  Measurements  and  Graphical  Methods 
(McGraw-Hill,  1913)  p.  19 

General  reviews  giving  also  a bibliography  of  portions  of  the 
literature  are: 

Zahn,  Jahrb.  f.  Rad.  5,  166,  1908 
J.  Clay,  Jahrb.  f.  Rad.  12,  273,  1915 

The  sections  on  this  topic  in  the  handbooks  of  Wiedemann, 
Winckelman,  and  Graetz 

Baedeker,  Elektrische  Erscheinungen  in  Metallischen  Leitern 
(Vieweg,  1911). 


* 


■ 


Table  1 


OBSERVATIONS  ON  THE  RESISTANCE  CHANGE  OF  #40  B & S COPPER  WIRE 
IN  A TRANSVERSE  MAGNETIC  FIELD 


Sensitivity 

R =-0.001  ohm 
Time  interval,  20  seconds 


D,  mm 
39.8 

AD 

^2 

8.8 

31.0 

0.5 

40.0 

31.2 

0.7 

4.1 

30.9 

0.4 

40.0 

30.9 

0.4 

8.6 

31.4 

0.9 

38.5 

29.9 

0.6 

8.1 

30.9 

0.1 

40.4 

31.7 

1.2 

10.8 

29.6 

0.9 

40.0 

29.2 

1.3 

7.7 

32.3 

1.8 

39.0 

31.3 

0.8 

10.6 

28.4 

2.1 

41.0 

30.4 

0.1 

Mean  value  of  AD  — 30.5  mm. 
The  probable  error  in  AD  is 
0.20  mm,  or  0.1%. 


Magnet  Energized 
for  Alternate  Readings 

i = 5.30  amp.  H = 11.1 

kilogausses 


D,  mm 
10.3 

AD 

^2 

29.8 

19.5 

2.2 

7.2 

22.6 

0.9 

26.2 

21.9 

0.2 

4.1 

22.1 

0.4 

26.0 

21.9 

0.2 

4.0 

22.0 

0.3 

24.7 

20.7 

1.0 

2.0 

22.7 

1.0 

24.3 

22.3 

0.6 

2.1 

22.1 

0.4 

24.1 

22.0 

0.3 

4.0 

20.1 

1.6 

25.9 

21.9 

0.2 

4.1 

21.8 

0.1 

26.0 

21.9 

0.2 

2.3 

23.7 

2.0 

Mean  value  of  AO  — 21.7  mm. 
The  probable  error  in  AD  is 
0.21  mm  or  1^. 


, ■ 


' 

. 


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50 


Table  2 


SUMMARY  OF  MEASUREMENTS  OF  THE  RESISTANCE  CHANGE 
OF  #40  B & S COPPER  WIRE  IN  THE  MAGNETIC  FIELD 


In  a Longitudinal  Magnetic  Field 


H 

AD 

AR 

AR 

AR 

kilogausses 

mm. 

ohms • 10“ 

R 10-5 

RH2 

4.64 

3.9 

1.22 

6.1 

2.84 

7.04 

8.1 

2.53 

12.7 

2.56 

9.82 

13.8 

4.31 

21.6 

2.24 

12.8 

23.2 

7.25 

36.3 

2.22 

16.4 

The  mean 

38.4 

value 

12.0 
°r  *i  * 

60.0 

is  2.40-10"7 

2.32 

In 

a Transverse  Magnetic 

Field 

H 

AD 

AR  -4 

AR 

kilogausses 

mm. 

ohms  • 10 

R 10“S 

RH2 

5.5 

5.5 

1.76 

8.8 

2.89 

8.4 

13.0 

4.28 

21.4 

3.06 

11.1 

21.7 

7.14 

35.7 

2.90 

12.9 

29.0 

9.26 

46.3 

2.79 

15.0 

37.3 

11.9 

59.5 

2.65 

The  mean 

value 

of  A+  ( = *”^c)  is 
t RH2' 

2.86-10  “7 

♦ 


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